Mrs Asher had a sum of money. If she bought 5 mini cupcakes and 7 chocolate bars, she would have $2 left. If she bought 3 mini cupcakes and 6 chocolate bars, she would have $12 left. Given that she had $54, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 chocolate bar = 1 C

5 M + 7 C + 2 = 54
5 M + 7 C = 54 - 2
5 M + 7 C = 52 ---- (1)

3 M + 6 C + 12 = 54
3 M + 6 C = 54 - 12 
3 M + 6 C = 42 ---- (2)

Make C the same.

(1) _{x 6}
30 M + 42 C = 312 ---- (3)

(2) _{x 7}
21 M + 42 C = 294 ---- (4)

(3) - (4) 
30 M - 21 M = 312 - 294
9 M = 18

1 M = 18 ÷ 9 = 2

Number of mini cupcakes that Mrs Asher can buy
= 54 ÷ 2
= 27 r 0

Most number of mini cupcakes that Mrs Asher can buy = 27

Answer(s): 27